Question

derive equation of internal energy of gas in terms of degree of freedom​

Answer 1

Explanation:

If heat exchange is zero then the process will be adiabatic and in that case the work done by the gas will NOT be equal to

nR(dT)

rather it will be equal to the expression given in the image. if you use the expression given in the image then you get the answer. I am also posting the proof calculation of work done in adiabatic process.

So that is where the problem is lying in your solution.